Problem: Is ${905421}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{9054} {21} = \gray{9054} \gray{00} + {21} $ Because $905400$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${21}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $21$ , divisible by $4$ No, $21$ is not divisible by $4$, so $905421$ is also not divisible by $4$.